Sir David Higgins at the opening of King's Cross Square in London. Photograph: Alessio Fiori/Barcroft Media

The person newly appointed to bring the HS2 project back on track, Sir David Higgins, has admitted the budget could be higher than £42.6bn.

And further doubts were cast on the high-speed rail project's cost by the mayor of London, Boris Johnson, who said necessary work in the capital was not accounted for and claimed that top Treasury figures had serious anxieties about the budget.

Higgins, the Network Rail boss who will become chairman of HS2 in 2014, said he did not know if the budget was realistic, adding: "It could be higher or lower. I haven't looked at it yet."

He said he did not expect to be in his new role for more than two years, but added that his tenure would correspond with the "most critical part of the project", when key decisions were made. He said his experience at the Olympic Delivery Authority showed that the shape of London 2012 was determined in the first 15 months of planning.

Higgins said he believed that the timescale of HS2 could be moved forward, saying: "We have some of the best construction designers and engineers in the world." During Thursday's opening of King's Cross Square, where work overnight had revealed the final stage of the transformation of the London station, he joked: "Why are we speaking about taking 20 years to build HS2 if this is what we can do in 24 hours?"

The first stage of HS2, from London to Birmingham, is due to be finished by 2026, with the second stage, including the extension to Manchester and Leeds, due to be completed by 2032.

He said having cross-party support was vital for HS2 to go ahead. Labour backs the scheme but the shadow chancellor, Ed Balls, has questioned whether it is "the best way to spend £50bn for the future of our country". The projected £50bn cost of HS2 includes the cost of new rolling stock.

Fears about the cost were compounded by the London mayor. Johnson said he was sure that Higgins would "deliver HS2 on time and on budget – whatever that budget eventually turns out to be".

The mayor added: "There are things we need to get straight. It is not yet clear how it's going to unite with Euston. We need to have more discussion about the link with HS1 – the plan to use the north London line would have traumatic effects."

Johnson said irrespective of all the questions about London, "anyone serious at the Treasury will tell you that they have anxieties about the budget".

However, the transport secretary, Patrick McLoughlin, said he was confident Higgins could ensure that the scheme came in within the £42.6bn price. "The budget has been set. It's a generous budget to do a proper job."

Earlier on Thursday, Higgins spelt out that his first priority was to get cross-party support, which he said proved absolutely crucial for the London Olympics. He told BBC Radio 4's Today programme: "The first thing I said to George Osborne was: 'There's only one thing I really need on this project: it has to be bipartisan' … The key thing is setting out the alternatives. While we do have the safest railway in Europe, we have the oldest railway in Europe … It [HS2] is essential for growth."

Higgins expressed confidence that the public and political opponents could be won over, noting that for all the success of the London Olympics, "there wasn't a single bit of positive media coverage [in 2006] … It took about two years for the first green shoots to emerge."

He said HS2 was about increasing capacity in the south and connectivity in the north, and that transport was central to regeneration. "Not doing this and expecting the northern cities to be more connected and therefore have greater economic growth is unrealistic."

John Harris: HS2, the UK's first high-speed rail link, is still years away, and could end up costing £70bn. For those on its route, uncertainty about what will happen to their homes is taking over their lives